How does the Heisenberg Uncertainty Principle affect the measurement of a particle's energy and momentum simultaneously?

The Heisenberg Uncertainty Principle says that certain pairs of quantities, like energy and time or position and momentum, cannot both be known exactly at the same time. For a particle, if you try to measure its energy very precisely, the uncertainty in its momentum increases, and vice versa. This happens because the act of measuring one property disturbs the other; mathematically, their operators do not commute, leading to a lower bound on the product of their uncertainties. For example, if you confine a particle to a tiny region of space, you know its position well but its momentum becomes highly uncertain, making its exact energy hard to determine. Thus, the principle limits how precisely we can simultaneously determine a particle’s energy and momentum.